Appendix A- AcadiaSupplementTrajectory analysis results atAcadia National Park.Equations for Different MetricsEveryday Residence-time Probabilityiestrajectorallfromcellsgridallthroughpassingendpointstotalji,cellgridthroughpassingendpointstotal===NnNnEPijijHigh Day Residence-time Probabilitytoriesday trajechighfromcellsgridallthroughpassingendpointsdayhightotalji,cellgridthroughpassingendpointsdayhightotal===MmMmHPijijIncremental ProbabilityEPHPIP−=Cluster-Weighted Probabilitydays)allon(basedionconcentratpollutantAveragei)clusterwithassociatednsobservatioon(basedionconcentratpollutantAverage)(calculatedclustersofnumbertotal)(11===⋅−⋅=∑=CCLEPCRPCCCWPiiLiiDescription of Figures• Central Trajectory (CT)- Trajectory with the largest number of nearest neighbors inthe dataset.• Frequency Based Clusters- These clusters are formedby finding the “central”trajectory which has the greatest number of neighboring trajectories within asubjectively selected radius of proximity (R). These trajectories are then removedfrom the dataset and the process is applied to theremaining trajectories.• Proximity Based Clusters- Clustering relies on thefrequency-based cluster groups,but forms trajectory groups based on proximity rather than frequency. In the firststep, the frequency-based approach is used to identify the central trajectories thatrepresent the most populated frequency-based clusters (approximately 10 clusterstypically contain at least 98% of the trajectoriesin the dataset using R=12 and 120hour back-trajectory (BT) time). These 10 centraltrajectories are then used todevelop 10 proximity-based clusters by assigning every trajectory in the dataset toits nearest central trajectories (calculated back to 72 hours).• Incremental Probability- Difference between the everyday probability (probabilityderived from all the trajectories in the dataset) and high day probability (probabilityderived from trajectories arriving at the site on the subset of high pollution days).• Cluster Weighted Probability- Each PATH-derived cluster’s residence-timeprobability is weighted by the average sulfate (orother pollutant) value for anymeasurements corresponding to a trajectory which isa member of that cluster.The weighted residence-time probability is summed overallclusters calculated fora site. The everyday probability is subtracted from the sum of cluster-weightedprobabilities to identify areas of increased (or inthe case of negative values,decreased) probability of being associated with a meteorological pathway forpollutant transport.Cluster 1 Cluster 2 Cluster 3 Cluster 4 Cluster 5Acadia All Trajectories 00-04, Top 10 ClustersModes defined at: R=12, 120hr BT,500mStart ht, 5111 Valid Trajectories, 9264 InvalidReassigned Trajectories Based on72hr BT,500m Start Ht, 8274 Valid Trajectories Frequency Based Cluster Proximity Based ClusterFrequency Based Cluster Frequency Based Cluster Frequency Based Cluster Frequency Based Cluster FrequencyBased ClusterProximity Based Cluster Proximity Based Cluster Proximity Based Cluster Proximity Based Cluster ProximityBased ClusterCentral TrajectoryCentral Trajectory Central Trajectory Central Trajectory Central TrajectoryFrequency ProximitySulfate 1.31 3.13Bext 30.24 57.88PM 3.86 7.80OC 1.15 1.58# Trajs 321 1165# Trajs w. Poll 97 389Frequency ProximitySulfate 1.30 1.40Bext 29.89 30.83PM 4.04 4.09OC 1.21 1.04# Trajs 487 1032# Trajs w. Poll 137 245Frequency ProximitySulfate 2.76 1.79Bext 54.39 39.91PM 6.92 5.42OC 1.36 1.49# Trajs 817 1058# Trajs w. Poll 221 302Frequency ProximitySulfate 2.17 3.14Bext 44.79 59.88PM 6.01 7.92OC 1.55 1.52# Trajs 1302 738# Trajs w. Poll 324 195Frequency ProximitySulfate 2.60 2.45Bext 52.19 50.35PM 6.91 6.54OC 1.63 1.57# Trajs 3811 1347# Trajs w. Poll 1056 373Cluster 6Frequency Based ClusterCluster 7 Cluster 8 Cluster 9 Cluster 10Acadia All Trajectories 00-04, Top 10 ClustersModes defined at: R=12, 120hr BT,500mStart ht, 5111 Valid Trajectories, 9264 InvalidReassigned Trajectories Based on72hr BT,500m Start Ht, 8274 Valid TrajectoriesFrequency Based Cluster Frequency Based Cluster Frequency Based Cluster Frequency Based ClusterProximity Based Cluster Proximity Based Cluster Proximity Based Cluster Proximity Based Cluster ProximityBased Cluster Frequency Based Cluster Proximity Based ClusterCentral TrajectoryCentral Trajectory Central Trajectory Central Trajectory Central TrajectoryFrequency ProximitySulfate 1.07 3.19Bext 22.28 64.16PM 2.85 8.19OC 0.75 1.91# Trajs 264 805# Trajs w. Poll 78 222Frequency ProximitySulfate 3.28 1.70Bext 59.81 33.20PM 8.02 4.25OC 1.46 0.81# Trajs 235 543# Trajs w. Poll 75 137Frequency ProximitySulfate 1.03 2.21Bext 23.62 44.48PM 3.23 6.11OC 1.10 1.52# Trajs 168 1177# Trajs w. Poll 23 331Frequency ProximitySulfate 1.50 2.10Bext 31.53 44.05PM 4.05 5.95OC 0.62 1.52# Trajs 122 1358# Trajs w. Poll 29 324Frequency ProximitySulfate 1.99 1.41Bext 46.99 28.96PM 5.59 3.78OC 1.25 0.89# Trajs 105 699# Trajs w. Poll 20 208Acadia All Trajectories 00-04, Best/Worst SulfateModes defined at: R=12, 120hr BT,500mStart ht, 5111 Valid Trajectories, 9264 InvalidReassigned Trajectories Based on72hr BT,500m Start Ht, 8274 Valid TrajectoriesLowest Sulfate(Proximity Based)Highest Sulfate(Proximity Based)Sulfate- Sulfate ion Conc. (ug/m3)Bext- Extinction (Mm-1)PM- Particulate Matter Conc. (ug/m3)OC- Organic Carbon Conc. (ug/m3)Num Trajs- Number of trajectories inclusterNum Trajs w. Poll- Number of trajectoriesin cluster with associated pollutionmeasurement (Based on number of IMPROVEsamples taken during the 2000-2004 period).Frequency ProximitySulfate 1.07 3.19Bext 22.28 64.16PM 2.85 8.19OC 0.75 1.91# Trajs 264 805# Trajs w. Poll 78 222Frequency ProximitySulfate 2.17 3.14Bext 44.79 59.88PM 6.01 7.92OC 1.55 1.52# Trajs 1302 738# Trajs w. Poll 324 195Frequency ProximitySulfate 1.30 1.40Bext 29.89 30.83PM 4.04 4.09OC 1.21 1.04# Trajs 487 1032# Trajs w. Poll 137 245Frequency ProximitySulfate 1.99 1.41Bext 46.99 28.96PM 5.59 3.78OC 1.25 0.89# Trajs 105 699# Trajs w. Poll 20 208Acadia All Trajectories 00-04, Incremental ProbabilityIP Based on Top10%500mSulfatePMOC B-extSulfate PM OC B-ext1000mAcadia All Trajectories 00-04, Cluster Weighted ProbabilityCalculated using Proximity Based Clusters, 500mSulfate PMOCB-extAcadia All Trajectories 00-04, Cluster Weighted ProbabilityCalculated using Frequency Based Clusters, 500mSulfate PMOCB-ext